Phase Transitions and Backbones of the Asymmetric Traveling Salesman Problem

In recent years, there has been much interest in phase transitions of combinatorial problems. Phase transitions have been successfully used to analyze combinatorial optimization problems, characterize their typical-case features and locate the hardest problem instances. In this paper, we study phase transitions of the asymmetric Traveling Salesman Problem (ATSP), an NP-hard combinatorial optimization problem that has many real-world applications. Using random instances of up to 1,500 cities in which intercity distances are uniformly distributed, we empirically show that many properties of the problem, including the optimal tour cost and backbone size, experience sharp transitions as the precision of intercity distances increases across a critical value. Our experimental results on the costs of the ATSP tours and assignment problem agree with the theoretical result that the asymptotic cost of assignment problem is pi ^2 /6 the number of cities goes to infinity. In addition, we show that the average computational cost of the well-known branch-and-bound subtour elimination algorithm for the problem also exhibits a thrashing behavior, transitioning from easy to difficult as the distance precision increases. These results answer positively an open question regarding the existence of phase transitions in the ATSP, and provide guidance on how difficult ATSP problem instances should be generated

LS 5039 - the counterpart of the unidentified MeV source GRO J1823-12

The COMPTEL experiment on CGRO observed the gamma-ray sky at energies from 0.75 MeV to 30 MeV between April 1991 and June 2000. COMPTEL detected many gamma-ray sources, among them an unidentified one labeled GRO J1823-12, which is positionally consistent with the prominent high-mass X-ray binary LS 5039. Because LS 5039 was established as gamma-ray emitter during recent years, whose gamma-radiation radiation is modulated along its binary orbit, we reanalysed the COMPTEL data of GRO J1823-12 including an orbital resolved analysis. We find a significant MeV source, showing evidence for a modulated MeV flux corresponding to the orbital period of LS 5039 of about 3.9 days. We show that its MeV emission is stronger at the orbital part around the inferior conjuction than at the part of the superior conjunction, being in phase with X-rays and TeV gamma-rays, however being in anti-phase with GeV gamma-rays. We conclude that the COMPTEL source GRO J1823-12 is the counterpart of the microquasar candidate LS 5039, at least for the majority of its MeV emission. The COMPTEL fluxes, put into multifrequency perspective, provide new constraints on the modelling of the high-energy emission of LS 5039.Comment: accepted by Astronomy & Astrophysics; 11 pages, 9 figure

Discussions of Racial Difference and the Effect on Client Ratings of the Working Alliance and Counselor

Fifty-one clients were surveyed to examine the effect of counselor discussion of racial and ethnic differences in counseling. Analyses revealed that White counselors who discussed these differences with their clients of color were rated as more credible and as having stronger working alliances than those who did not discuss such differences. Se entrevistó a cincuenta y un clientes para examinar los efectos de la discusión por parte del consejero de las diferencias raciales y étnicas en consejería. L os análisis revelaron que los consejeros Blancos que discutieron estas diferencias con sus clientes de color fueron valorados como más fiables y con alianzas de trabajo más sólidas que aquellos que no discutieron tales diferencias

Mechanical Properties of Phosphorene Nanotubes: A Density Functional Tight-Binding Study

Using density functional tight-binding method, we studied the elastic properties, deformation and failure of armchair (AC) and zigzag (ZZ) phosphorene nano tubes (PNTs) under uniaxial tensile strain. We found that the deformation and failure of PNTs are very anisotropic. For ZZ PNTs, three deformation phases are recognized: The primary linear elastic phase, which is associated with the interactions between the neighboring puckers, succeeded by the bond rotation phase, where the puckered configuration of phosphorene is smoothed via bond rotation, and lastly the bond elongation phase, where the P-P bonds are directly stretched up to the maximally allowed limit and the failure is initiated by the rupture of the most stretched bonds

An Active Set Algorithm for Nonlinear Optimization with Polyhedral Constraints

A polyhedral active set algorithm PASA is developed for solving a nonlinear optimization problem whose feasible set is a polyhedron. Phase one of the algorithm is the gradient projection method, while phase two is any algorithm for solving a linearly constrained optimization problem. Rules are provided for branching between the two phases. Global convergence to a stationary point is established, while asymptotically PASA performs only phase two when either a nondegeneracy assumption holds, or the active constraints are linearly independent and a strong second-order sufficient optimality condition holds

The Silicon Meta-shell X-ray Mirror Technology Development Roadmap for the Lynx Mission

This document presents a roadmap for advancing the silicon meta-shell optics (SMO). It describes an overall strategy and key technical elements to be developed to meet the four-fold Lynx requirements: (1) angular resolution, (2) effective area, (3) mass, and (4) production schedule and cost. It also describes the building and testing of an engineering unit whose successful completion will retire all risks, technical, logistical, schedule, and cost, associated with building and delivering a mirror assembly for the Lynx mission. All of this work, designed to advance this technology to TRL 6, will be completed by Preliminary Design Review (PDR) to ensure that the flight mirror assembly production process will be but a repetition of a set of well-defined and mature steps, leading to on-time and on-budget delivery of a mirror assembly for the Lynx mission